Tommy Fury has accused Jake Paul of instigating a backstage scuffle “for the cameras” and has claimed his rival might never return to the ring.
Paul and his manager insisted a future fight with Fury "doesn't make sense" after they clashed in a corridor following their respective wins on Sunday night.
YouTuber-turned-boxer Paul noted his eight-round fight was double the duration of Fury's, then said about their confrontation: "The guy had nothing to say. He had a mediocre performance against my sparring partner.
"Fury is supposed to be this big, tough guy from a legendary bloodline but I got in his face.
"I hired him to be here. I gave him an opportunity to shine.
"He is an easier fight than Tyron Woodley.
"People say he is a 'real boxer' so let's run it."
The younger brother of Tyson Fury said about his backstage row with Paul: "The man can say what he wants about my performance, but he went eight rounds against a guy who just walked forwards and didn't throw a shot.
"Tyron nearly knocked Jake out.
"Will we see Jake in the ring again? I don't think he has [guts]. It's obvious.
"He was asked about me but had nothing to say.
"He confronted me in the hallway with a team of 15-20, jumping all over us. We were ready to fight.
"I was ready to throw hands. He doesn't understand that me and my team will go now. We'll get stuck in.
"His security broke it up because he can't fight. Imagine him in a street fight! Please. He can't fight.
"If he didn't have his security team with him, he would have walked straight past me.
"He is big in front of cameras but small by himself.
"There was a moment in that corridor, when everything was going off between his security and my team, that it was just me and him.
"I looked dead into his soul. If the cameras aren't around, he doesn't want to know."
Paul was non-committal on his boxing future, insisting after four pro fights inside two years he might take a rest.
Fury claimed the big right hand that Paul absorbed from Woodley, which knocked him into the ropes, has taught him a lesson.
"Jake realised tonight how hard the sport of boxing is, and he only got hit by a little shot," Fury said. "Imagine if he got dropped.
"I don't know if you'll see Jake in the ring again."
Fury claimed he was blocked from climbing into the ring to challenge Paul: "They ain't fighters. If you want the fight, I'm ready to go. No running, no playing.
"It's fine if you don't want the fight. Just say it. Put everyone's mind at rest.
"I want the fight.
"I've done my part, he did his part. Why not make the fight next? It's on the tip of everyone's tongues."
Paul said about a tweet posted by Conor McGregor that appeared to refer to his fight: "We're on the path to bigger fights. I'm salivating too.
"I have five wins in a row, he is 1-3 in the past four years. There is no way he hits harder than Woodley. He doesn't weigh as much as Woodley. Woodley is a harder fight than Conor.
"Conor is going down. I'm going up."
He added: "I'm saying this as humbly as possible - no one has done fights as big as this in their fourth fight in boxing history.
"No one watched Floyd Mayweather's fourth fight. Saul 'Canelo' Alvarez took on someone who was 0-0 in his 10th fight.
"I'm taking on world champions, a five-time UFC champion, selling out an arena in my hometown."